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Matrix Logic Problem 1

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The way to solve this type of puzzle is to make a matrix (grid) of the facts you are given. This first week we'll make it fairly easy so you can see how they work, then we'll get harder.

Five students (Josh, Becca, Romy, Ian, and Julia) compared their scores on a math test. Their math scores were 100, 98, 96, 80, and 78. Use the clues to match each person with their score.

Clues:
  1. Josh scored higher than Julia and Ian.
  2. Romy's score was 20 more than Ian's but less than Becca's
Here's a grid for this problem:

100 98 96
80
78
Josh √ √
Becca
Romy
Ian
Julia

Put a √ in each box that can't be true. For instance, from the clues, you know that Josh can't be the lowest score, or even the second lowest, since he scored higher than Julia and Ian. So we've put √s in those boxes.

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